Sensitivity analysis for the sample size planning method with the goal to obtain sufficiently narrow confidence intervals for standardized ANCOVA complex contrasts.
ss.aipe.sc.ancova.sensitivity(true.psi = NULL, estimated.psi = NULL,
c.weights, desired.width = NULL, selected.n = NULL, mu.x = 0,
sigma.x = 1, rho, divisor = "s.ancova", assurance = NULL,
conf.level = 0.95, G = 10000, print.iter = TRUE, detail = TRUE, ...)the population standardized ANCOVA contrast
the estimated standardized ANCOVA contrast
the contrast weights
the desired full width of the obtained confidence interval
selected sample size to use in order to determine distributional properties of a given value of sample size
the population mean for the covariate
the population standard deviation of the covariate
the population correlation coefficient between the response and the covariate
which error standard deviation to be used in standardizing the contrast; the value can be
either "s.ancova" or "s.anova"
parameter to ensure that the obtained confidence interval width is narrower than the
desired width with a specified degree of certainty (must be NULL or between zero and unity)
the desired confidence interval coverage, (i.e., 1 - Type I error rate)
number of generations (i.e., replications) of the simulation
to print the current value of the iterations
whether the user needs a detailed (TRUE) or brief (FALSE) report of the simulation results; the
detail report includes all the raw data in the simulations
allows one to potentially include parameter values for inner functions
observed standardized contrast in each iteration
vector of the full confidence interval width
vector of the lower confidence interval width
vector of the upper confidence interval width
iterations where a Type I error occurred on the upper end of the confidence interval
iterations where a Type I error occurred on the lower end of the confidence interval
iterations where a Type I error happens
the lower limit of the obtained confidence interval
the upper limit of the obtained confidence interval
number of replications of the simulation
population standardized contrast
estimated standardized contrast
the desired full width of the obtained confidence interval
the value assigned to the argument assurance
sample size per group
number of groups
mean width of the obtained full confidence intervals
median width of the obtained full confidence intervals
standard deviation of the widths of the obtained full confidence intervals
percentage of the obtained full confidence interval widths that are narrower than the desired width
mean lower width of the obtained confidence intervals
mean upper width of the obtained confidence intervals
Type I error rate from the upper side
Type I error rate from the lower side
Type I error rate
The sample size planning method this function is based on is developed in the context of simple (i.e., one-response-one-covariate) ANCOVA model and randomized design (i.e., same population covariate mean across groups).
An ANCOVA contrast can be standardized in at least two ways: (a) divided by the error standard deviation of the ANOVA model, (b) divided by the error standard deviation of the ANCOVA model. This function can be used to analyze both types of standardized ANCOVA contrasts.
The population mean and standard deviation of the covariate does not affect the sample size planning procedure; they can be specified as any values that are considered as reasonable by the user.
Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1--24.
Kelley, K., & Rausch, J. R. (2006). Sample size planning for the standardized mean difference: Accuracy in Parameter Estimation via narrow confidence intervals. Psychological Methods, 11 (4), 363--385.
Lai, K., & Kelley, K. (2012). Accuracy in parameter estimation for ANCOVA and ANOVA contrasts: Sample size planning via narrow confidence intervals. British Journal of Mathematical and Statistical Psychology, 65, 350--370.
Steiger, J. H., & Fouladi, R. T. (1997). Noncentrality interval estimation and the evaluation of statistical methods. In L. L. Harlow, S. A. Mulaik, & J.H. Steiger (Eds.), What if there were no significance tests? (pp. 221--257). Mahwah, NJ: Lawrence Erlbaum.